We study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T, where the labels v1, v2, v3, . . . on every path starting at the root of T satisfy v...
Abstract. Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. One important problem in ...
The Baxter number Bn can be written as Bn = n k=0 Θk,n−k−1 with Θk,ℓ = 2 (k + 1)2 (k + 2) k + ℓ k k + ℓ + 1 k k + ℓ + 2 k . These numbers have first appeared in the...
We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian's Fast Marching Method and Polthier's Straightest Geodesics theory, w...
Let Tn denote the set of triangulations of a convex polygon K with n sides. We study functions that measure very natural "geometric" features of a triangulation Tn, fo...
Luc Devroye, Philippe Flajolet, Ferran Hurtado, Ma...